Would there be any value in having available a second kind of empty?
The main difference I see between a true empty and a mesh object without any geometry is that the empty-mesh can emit particles, and can get the entire range of physics types (although it will be useless for many of them without its geometry).

The interesting bit is that as an emitter, the mesh will emit only from its origin, and particles will fall in a straight ordered line - a potentially useful effect.

Both a true empty and the empty-mesh can receive the same constraints, and most modifiers will do absolutely nothing on the empty-mesh. It could be useful to parent the empty-mesh to an armature (directly to a bone, otherwise it won't be affected since it has no verts and no weights), but you can get the same effect with a real empty by parenting it to an individual bone.

So, particles and some types of physics is the only thing I can see that makes a real difference.